Stochastic gradient descent-based inference for dynamic network models with attractors

In Coevolving Latent Space Networks with Attractors (CLSNA) models, nodes in a latent space represent social actors, and edges indicate their dynamic interactions. Attractors are added at the latent level to capture the notion of attractive and repulsive forces between nodes, borrowing from dynamical systems theory. However, CLSNA reliance on MCMC estimation makes scaling difficult, and the requirement for nodes to be present throughout the study period limit practical applications. We address these issues by (i) introducing a Stochastic gradient descent (SGD) parameter estimation method, (ii) developing a novel approach for uncertainty quantification using SGD, and (iii) extending the model to allow nodes to join and leave over time. Simulation results show that our extensions result in little loss of accuracy compared to MCMC, but can scale to much larger networks. We apply our approach to the longitudinal social networks of members of US Congress on the social media platform X. Accounting for node dynamics overcomes selection bias in the network and uncovers uniquely and increasingly repulsive forces within the Republican Party. Supplemental materials for the article are available online.

在带吸引子的协同演化隐空间网络（Coevolving Latent Space Networks with Attractors, CLSNA）模型中，隐空间内的节点代表社会行动者，边则表征二者之间的动态互动。研究借鉴动力学系统理论，在隐空间层面引入吸引子，以刻画节点间的吸引与排斥作用力概念。然而，CLSNA依赖马尔可夫链蒙特卡洛（Markov Chain Monte Carlo, MCMC）进行参数估计，导致其难以扩展至大规模网络；同时模型要求节点在整个研究周期内始终存在，这一限制也制约了其实际应用场景。针对上述问题，本文从三方面进行改进：(1) 引入随机梯度下降（Stochastic gradient descent, SGD）参数估计方法；(2) 提出一种基于SGD的不确定性量化新方法；(3) 对模型进行扩展，允许节点随时间动态加入或退出网络。仿真实验结果表明，相较于MCMC方法，本文提出的扩展模型仅存在微小的精度损失，却可适配规模大得多的网络。我们将所提方法应用于美国国会议员在社交媒体平台X上的纵向社交网络数据集。考虑节点动态变化特性后，不仅有效克服了网络中的选择偏差问题，还揭示出共和党内部独特且持续增强的排斥作用力。本文的补充材料可在线获取。